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This page covers Questions and Worked Solutions for Edexcel Pure Maths Paper 2 October 2020, 9MA0/02.

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Edexcel 2020 Pure Maths Paper 2 Question Paper (pdf)

Edexcel 2020 Pure Maths Paper 2 Mark Scheme (pdf)

- The table below shows corresponding values of x and y for y =

The values of y are given to 4 significant figures.

(a) Use the trapezium rule, with all the values of y in the table, to find an estimate for giving your answer to 3 significant figures. - Relative to a fixed origin, points P, Q and R have position vectors p, q and r respectively.

Given that

- P, Q and R lie on a straight line
- Q lies one third of the way from P to R

show that q = 1/3(r + 2p)

- (a) Given that

2log (4 − x) = log(x + 8)

show that

x^{2}− 9x + 8 = 0

(b) (i) Write down the roots of the equation

x^{2}− 9x + 8 = 0

(ii) State which of the roots in (b)(i) is not a solution of

2log(4 − x) = log(x + 8)

giving a reason for your answer.

- In the binomial expansion of

(a + 2x)^{7}

where a is a constant

the coefficient of x^{4}is 15 120

Find the value of a. - The curve with equation y = 3 × 2
^{x}

meets the curve with equation y = 15 − 2^{x+1}at the point P.

Find, using algebra, the exact x coordinate of P. - (a) Given that

find the values of the constants A, B and C - Figure 1 shows a sketch of the curve C with equation
- A curve C has equation y = f(x)

Given that

- fʹ(x) = 6x
^{2}+ ax − 23 where a is a constant - the y intercept of C is −12
- (x + 4) is a factor of f(x)
find, in simplest form, f(x)

- A quantity of ethanol was heated until it reached boiling point.

The temperature of the ethanol, θ °C, at time t seconds after heating began, is modelled by the equation

θ = A − Be^{−0.07t}

where A and B are positive constants.

Given that

- the initial temperature of the ethanol was 18°C
- after 10 seconds the temperature of the ethanol was 44°C

(a) find a complete equation for the model, giving the values of A and B to 3 significant figures.

Ethanol has a boiling point of approximately 78°C

(b) Use this information to evaluate the model.

- (a) Show that

cos 3A ≡ 4cos^{3}A − 3 cosA

(b) Hence solve, for −90° x 180°, the equation

1 − cos3x = sin2 x - Figure 2 shows a sketch of the graph with equation

y = 2 | x + 4| − 5

The vertex of the graph is at the point P, shown in Figure 2.

(a) Find the coordinates of P.

(b) Solve the equation

3x + 40 = 2 | x + 4| − 5

A line l has equation y = ax, where a is a constant.

Given that l intersects y = 2| x + 4| − 5 at least once,

(c) find the range of possible values of a, writing your answer in set notation. - The curve shown in Figure 3 has parametric equations

x = 6sint y = 5 sin 2t 0 t π/2

The region R, shown shaded in Figure 3, is bounded by the curve and the x-axis. - The function g is defined by
- A circle C with radius r

- lies only in the 1st quadrant
- touches the x-axis and touches the y-axis

The line l has equation 2x + y = 12

(a) Show that the x coordinates of the points of intersection of l with C satisfy

5x^{2}+ (2r − 48) x + (r^{2}− 24r + 144) = 0

Given also that l is a tangent to C,

(b) find the two possible values of r, giving your answers as fully simplified surds.

- A geometric series has common ratio r and first term a.

Given r ≠ 1 and a ≠ 0

(a) prove that

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